Angular rate bombing system

ABSTRACT

An angular rate bombing system (ARBS) which utilizes angular rate and angle measurements from an automatic target tracker, pitch and roll information from a standard vertical gyro, true airspeed data and angle of attack information to compute an azimuth lead angle to release ordnance at the correct elevation lead angle.

United States Patent Cole [451 Oct. 17, 1972 [54] ANGULAR RATE BOMBING SYSTEM 2,819,461 l/1958 Bryan ..-.235/6l.5 E 72 I en R R0 D.C l L k C Hammond, J1. R 1 o y o m a e 3,264,451 8/1966 Faxen et al .235/615 R 1 Asslgneer The United States of America 88 2,825,055 2/1958 Chance ..235/6l.5 D represented y the Secretary of the 2,995,984 8/1961 l-lelgeson et al ..89/l.5 E Navy 3,288,984 11/1966 Bernier et al. ..235/6l.5 R

[22] Filed: Nov. 6,1970 Primary Examiner-Felix D. Gruber [21] Appl 87,519 Attorney-R. S. Sciascia and Roy Miller [52] us. Cl "235/615 1), 89/l.5 E, 235/615 E [5 ABSTRACT .[511 int. Cl. ..-..G06g 7/80 An an 1 gu at rate bombing system (ARBS) which util- [58] Field of Search ..235/6l.5 R, 61.5 1 61.5 1%: izes anguar rate and angle measutcmems from an 235/615 89/l'5 tomatic target tracker, pitch and roll information from a standard vertical gyro, true airspeed data and angle [56] Rflerences Cited of attack information to compute an azimuth lead UNITED STATES PATENTS angle to release ordnance at the correct elevation lead l 3,033,084 5/1962 Wheeler et al ..89ll .5 E ang e 2,737,652 3/1956 White et a1 ..'....235/6l.5 E 5 Claims, 14 Drawing Figures AUTOMATIC 'i COO DINATE 40 SIGHT TRACKER RESOLUTION UNIT RELEAsE XQ V COMPUTER VERTICAL REFERENCE x N w ANGLE E OF ATTACK f E PILOT'S NORMAL CONTROL ACCELERATION BOX PATENTED 3.699.310

SHEET 01 0F 10 AUTOMATIC h i COORDINATE M1 SIGHT TRACKER RESOLUTION UN IT RELEASE TRUE u AIR SPEED I COMPUTER VERTICAL REFERENCE 1 N w ANGLE E OF ATTACK 3 PILOT'S NORMAL CONTROL ACCELERATION BOX FIG. 'I.

\ FIG. 2 (O).

TWO DIMENSIONS RI, r

l N VEN TOR.

ROY D. COLE BY ROY MILLER ATTORNEY.

PATENTEDUBI 1 I9 2 3.699.310

SHEET 020F 10 FIG. 2m.

3' T A THREE DIMENSIONS AIRCRAFT ROLL AXIS Z TARGET (AT RELEASE) Y (VERTICAL) AIRCRAFT ROLL AXIS k TRACKER TARGET PATENfl-jnnm'mszz 3.699.310

SHEET 03UF1O Y(VERTICAL) e 3 11 Al RCRAFT ROLL AXIS Z TARGET (CIP) TRACKER TARGET PATENTEU I973 3,699,310

SHEET 0% 0F 10 TARGET (IMPACT POINT) k TRACKER TARGET FIG. 7.

PATENTED N 1 7 I373 SHEET UBUF 10 v wOO 00 mmr 29.55am mo SEE. omik AU WOO PAIENTED B I 3.699.310

SHEET 09 0F 10 AZIMUTH LEAD ANGLE ALL MODES E0 I26 AUTOMATIC TRACKER (FIG I) COMPUTATION AUTOMATIC "'id RELEASE EQUATION E0 138 BOMB ALL MODES RELEASE MODE CONTROL BALLISTIC EQUATIONS ALL MODES E0 2, 7, 125

VERTICAL REFERENCE (FIG II STICK DELIVERY ALL MODES ED 129, 130, 131 133. I25

'ALL cAL COORDINA PILOT RESOLUTION CONTROL (H6 1) BOX CONTROL (FIG 1) RACK DELAY AND u) TERMS ALL MODES E0 132, 136

TRUE AIRSPEED (FIG I) EJECTION TERMS ALL MODES EQ I34, 135, I39, I25

ANGLE OF ATTACK IFIG II CIP LEAD ANGLE CIP MODE EQ I28, I25

vNORMAL ACCELERATION (FIG II CRR LEAD ANGLE CRR/A MODE EQ I39, I45. I25

Fig. 9

PATENTED 3,699,310 sum lUUF 1o TARGET FIG.IO.

ANGULAR RATE BOMBING SYSTEM BACKGROUND OF THE INVENTION Typical standard bombing systems require range-totarget and velocity (direction and magnitude) inputs. Bombing accuracy is basically a function of how accurate these inputs are. At first, airspeed and barometric altitude were used; next, these inputs were improved by using radar range; and then, Doppler-inertial velocity was used. It is a matter of history that each step in the improvement of bombing capability (accuracy, flexibility, or versatility) causes an escalation in system cost and complexity; and finally, the point is reached at which thev increase in cost and complexity is unfavorably disproportionate to the increase in performance. Thispoint appears to have been passed in some sophisticated systems.

Recent advances in air-to-ground tracking systems offer the possibility of approaching the practical limit of bombing accuracy while avoiding the problems of the standard bombing system. The mathematical sophistication inherent in a tracker-based system accounts for a decrease in hardware complexity and a concomitant increase in reliability through elimination of the need for inputs from inertial navigation and radar systems. The low levelof complexity, plus today's microminiaturization techniques, allows a complete daylight bombing system to occupy a volume of less than 1 cu. ft.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a simplified block diagram of the invention;

FIG. 2(a) is a graph illustrating bomb ballistic coordinates in two dimensions;

FIG. 2(b) illustrates the bomb ballistic coordinates in three dimensions; 7

FIG. 3 illustrates the coordinates for a three axis tracker;

FIG. 4 is another illustration of the coordinates for a three axis tracker;

FIG. 5 illustrates the coordinates for a CIP attack;

FIG. 6 illustrates stick bombing graphically;

HO. 7 illustrates an alternate tracker coordinate system;

FIG. 8 (FIGS. 8A, 8B, 8C and 8D taken together) is a functional schematic of a computer used in the present invention;

FIG. 9 is a computational sub-section block diagram correlating FIG. 8 with the equations in the specification; and

FIG. 10 illustrates bomb ballistic coordinates in the vertical plane for CRR/A.

DESCRlPTlON OF THE. PREFERRED EMBODIMENT The ability of an optical-TV tracker, operating in the visible spectrum, to lock on and automatically track targets having sufficient contrast to be detectable and recognizable by a pilot has been amply demonstrated. Such a target-tracking device, with proven ability to track tactical ground targets from moving aircraft, is applicable to an angular rate bombing system (ARBS) such as described here. The major benefits of such a system are as follows:

1. It is a relatively simple, small bombing system that has a high, inherent delivery accuracy.

2. Wind and target motion are both automatically accounted for in the solution without requiring an explicit measurement of target or aircraft ground velocity,

thereby eliminating the need for ground velocity sensors. A range-to-target measurement is .not required, thus eliminating the need for radar or laser air-toground ranging systems.

3. The development of .laser (and beacon) targetdesignation schemes will give a semiblind bombing capability.

The ARBS is inherently a mode-less" weapondelivery system in that it will provide an automatic weapon-release signal whenever the measured (elevation) rate of the line-of-sight to the target equals the computed rate needed to obtain a hit. The system does not care how the aircraft reaches this condition; thus, the pilot can pursue any type of reasonable attack he chooses. The tactics include dive-toss, dive or glide,

.and medium-. and low-altitude level deliveries. Stick bombing is available with any of these forms of delivery.

TYPICAL ATTACK (COMPUTED AZIMUTH LEAD, AUTOMATIC RELEASEXCALIA) The sequence of events for a typical daylight attack is as follows. After the pilot visually detects and identifies the target, he dives the aircraft to put the(inertially stabilized) sighting pipper on the target. (The tracker axis is aligned with the sighting pipper.) When the pilot is sighting on the target, he pushes the lock-on button. The tracker then tracks the target automatically, and the computer generates the azimuth tracking commands and release signal. After lock-on, the movable reticle in the servoed sight is slaved to the tracking head so that sight-pip'tracking in elevation is accomplished automatically. However, the reticle is displaced in azimuth in an amount sufficient to correct for crossrange wind and target motion, and the pilot must steer in azimuth to put the reticle on the target. Weapon release occurs automatically. From the lock-on point, the pilot may pursue any tactic he desires. For a glide attack, he may pull up slightly immediately after lockon to establish a desired flight path. To convert to a toss attack, the pilot needs only to pull up at any point in the attack he chooses. Release will occur at the proper time.

TYPICAL ATTACK (CIP DELIVERY-MANUAL RELEASE) Using the computed impact point (CIP) delivery, the sequence of events in an attack is as follows. After visually detecting and identifying the target, the pilot dives the aircraft such that the sighting pip is on or near the target. He pushes the lock-on button. The tracker tracks this point automatically, and the computer generates the azimuth and elevation lead angles. These angles, displayed on the sight unit, tell where the bomb 1 (In CIP displays the pilot should not track the target but should move the sight pip through the target at a reasonable angular rate, as he does in present noncomputer attacks.)

TYPICAL ATTACK (CIP DELIVERY-AUTOMATIC RELEASE) The response time problem as described above suggests another (and possibly the best) method of delivery. It is the automatic release with a CI? display. Here, the pilot initially locks the sight pip (tracker) on the target, and the display is the computed bomb impact point. The aircraft is flown so asto move the pip over the target. The release is automatic(based on elevation rate). (Note that the pilot would not have to allow" an automatic release until just before the pip approaches the target.)

This latter form of operation will permit maneuvers (within the limit of the tracker gimbals) without the pilot response-time problems.

CHOSEN RELEASE RANGE, AUTOMATIC RELEASE (CRR/A) Often it is desired to release weapons at a prechosen altitude or slant range. While this may be done for various reasons, generally it is aimed at improving accuracy by getting as close to the target before release as is safe (from enemy fire, ground collision, weapon effects). For example, retarded weapons, such as the Mk 82 with Mk l5 Snakeye fin retarded, for best results should be released at from 1,500 to 2,500 feet slant range (depending on speed). At shorter ranges the fins are not open long enough, and for longer ranges the time of flight is too long.

..In this mode, after lock on, the pilot is to fly so as to put the sight pip on the target and track until release. This is the only delivery in which the pilot is asked to track the target with the sight pip. This CRR flight path is approximately a straight line or a slightly upward (positive g) curved path. Some maneuver is allowed.

ARBS USE WITH TARGET DESIGNATION SYSTEMS For daylight operation the TV-ARBS weapon delivery system can be used basically as is. A target designation system (TDS) would furnish the TV tracker the direction to the target. The tracker would lock onto and track whatever optical contrast that is present at the indicated target position.

The presentation to the pilot would be dependent on the type of servo sight used.

a. If the sight unit in the aircraft has two movable controlled pips, one of these would indicate the target position. The other (standard CIP display) pip would indicate the bomb impact point as in a CI? delivery. The pilot flies so as to move the bomb impact point over the target indicator pip. Release is at this time. An alternate would be to use the TDS to indicate target position on the sight unit and have the tracker lock onto contrast at or near the target. Then use the standard ARBS CIP display with a manual release.

b. One movable pip is sufficient in actual use. The impact point (CIP) pip would be positioned relative to the sight's fixed pip (as if it were the target) and the pilot flies to move this CIP pip over the fixedpip for release.

For day-night operations a, say, laser target designation system should have its own angular rate tracker and thus furnish an alternate source of angles and rates to the ARBS.

SYSTEM HARDWARE DESIGN The keynote of the ARBS scheme is simplicity. This is carried out in the hardware design as indicated by the 3 number of components (see FIG. 1). Measuring devices already utilized in standard aircraft flight equipment are used as much as is practical.

The heart of the ARBS is a gyro-stabilized optical- TV tracking head. Such trackers are described in U.S. Pat. Nos. 3,257,505 and 3,341,653. When locked on and tracking a target, the tracker provides the target line-of-sight rates and angles. These inputs, combined with air data and vertical information from standard aircraftequipment, are used to compute the instantaneous angular rate required for the weapon to impact the target. Bomb release occurs when this rate and the measured rate are the same.

The primary components and inputs to the system of FIG. 1 are:

a. Automatic Target Tracker. This is a TV contrast tracker similar to that used in the Walleye weapon. This input furnishes angular rate (an, 0),) and angles (5, "1)- b. Vertical Reference. A standard aircraft vertical gyro is used to furnish pitch (8) and roll (d1) information. In a highly maneuvering aircraft an improved erecting system may be desired, but is not necessary.

0. True Airspeed. A standard true airspeed measuring device is used to furnish magnitude of velocity (U) data.

Secondary or optional inputs may be also provided. However, these inputs are not absolutely necessary, but are desirable in that they increase stability and refine system accuracy. Also, they are normally already present in the aircraft.

These inputs are:

a. Angle of Attack (a). Angle of attack is used in' weapon drag factors (\11, 1 calculation, in the azimuth lead angle, and to eliminate the need of a filter in the CIP elevation lead angle calculation. [A one degree error in angle of attack causes negligible impact error for most low-drag bomb deliveries] b. Pressure Altitude (H or Static Pressure. Pressure altitude is used to compute density for air drag on the weapon. A hand set approximate target altitude could be used in its place. Altitude is not used in ARBS.

c. Normal Acceleration. (K Normal acceleration and angle of attack are inputs to a filter which is used to refine and stabilize the automatic tracker data. Only nominal accuracy is required for this use.

BALLISYTIC EQUATIONS ELEVATION LEAD ANGLE In solving for the bomb trajectory, it is assumed that the only forces acting on the bomb after release are gravity and air drag along the direction of the air-mass velocity. Here, the effect of wind on the trajectory is restricted to the vertical plane containing the air-mass velocity vector; crosswind is considered later. The wind structure is assumed to be uniform and equal to the wind velocity at release. These assumptions give the following ballistic (For vacuum conditions, the standard equation is sin y,.= (gR, cos 0',/2 V, cos8,) equations where:

' s'iny, (gRuII, coso-JZ V, cos8,)

\l1,.tI1[(k,U sin'y, seco',-k )f( W)] 2) where k, and k, are constants, U is the true airspeed, and Wis the range wing.

From FIGS. 2a and b note that I 'r u B2v' where 6, accounts for release ejection effects, a, is the angle 1 between the forward axis of the aircraft and the R, V, cos 6, (9)

where V is the azimuth (crosswind) component of velocity.

COORDINATE SYSTEMS There are several coordinate systems used in describing the present invention. All, except the air-mass system, are translating with the attacking aircrafts velocity (V) relative to the tracked point (target). FIG. 3 is useful in discussing four of the systems used in deriving the equations used in ARBS. An alternate tracker coordinate system is illustrated in FIG. 1 and will be referred to later in the discussion. The coordinates of FIG. 1 were used in the computer block diagram of FIG. 8.

Tracking Coordinates (i, j, k)

These are defined as i, j, k with the, unit vector k along the tracker forward axis (ideallytoward the (tracker) target); i along the inner gimbal; and j given by k X i. This is the coordinate system in which the rate measurement is made.

The coordinate origin is moving with the attacking aircraft velocity.

Aircraft Coordinates (m. n, I Axes) These are used here as I along theforw rd aircraft axis, m along left wing (I to I), and-n given by l X m. Thus, when the aircraft is horizontal, n is vertical.

Vertical Plane Reference Coordinate (e,, e,, e,)

This is a translating (with V) nonrotating nonaccelerating system in which two of the axes are in a vertical plane that contains the aircraft I axis. The coordinate system is defined only at the time of weapon release. The e, axis is along I and the c, axis is perpendicular to e, in the above vertical plane. The e,direction is such that e, e; X e,. These axes are the aircraft axes (m, n, I) if the roll angle, is zero.

This coordinate system is selected for use in the tire control system (a three-axis tracker) to compute necessary lead angles.

AIR-MASS COORDINATES The bomb drag is computed in air-mass coordinates. This reference system differs from the e,, e,, e, coordinates because of wind.

where i]: and 0 are measured at the tracker gimbals.

m cos 4: sin 0 e, n sin (1: cos 0) e, l 0 0 1 e,

where tii'liibiibi isdmpBdiFoiii digkihiZH is the measured aircraft roll angle.

' AIRCRAFT-TARGET VELOCITY The relative velocity (V) of the target in the homecelerating tracker coordinates (see Tracking Coordinates) is givenby the equation V 17 +2; x F

where 17,75, andTare measured in the rotating tracker coordinates. T 'is the apparent velocity (5 is the angular rate of coordinate system 7is the radius vector to the target Thus, if one assumes the tracker istracking the targe perfectly,

r'= rk 7 21 an, 1, components (The value of (0,, while it can be measured by a separate gyro on the platform, is not directly determined by the target tracking device. In the case of a two-axis tracker this w would be nearly the roll rate (dz). For the coordinates such as in FIG. 2, the magnitude of w, is generally small in a bombing attack. The actual 7 value of ou can be determined using the dive angle (8,) and the target angles (ti: and 6).) of Z) are the rate (ideally) measured in the tracker gyros. Thus, Equation 20 becomes V=(D,ri rj+ This velocity in the e e e coordinates is V cos ,0 sin 0 sin (1 cos 0 sin b I (V 0 cos 0 -sin 0 w;r

V s in 0 sin 6 cos (1 cos 0 cos r (24) V my cost! an! sine simll icos0 sindl 25 V o,r cost} r' sin0 (26) V w,r sine costli am sin0 coszbi cos0 cos 4am Thus,

or for V i-,

um' cos p 1+a tan 0 Mn (6+QK) V3 w T sin where 01; V COS0/i' 34 From equations 25, 26, and 31 Equations 33 and 36 are used with the bomb lead angle (equations 1 and 9) to make the bombing system equation.

COMMENTS, ASSUMPTIONS, AND

APPROXIMATIONS The following comments apply primarily to the computed lead angle mode of operation.

' w-r sin 0 1+0. tan a +5111 (36) The angle ll! is small, usually less than l00milliradians. Thus, in many places the cosine is used as l, and the sine or tangent can be used as til. However, ii: may be either plus or minus. (41 is limited to the tracking gimbal limits, e.g., i30, but is small when the pilot is near a release condition.)

The angle 0 will be positive since one needs to fly above the target (and tracked point) to measure an angular rate, which is required for correct release lead angle. The value of 0, to the target will be fairly small since the pilot must be able to see the target over the aircraft nose. The value of 6 to the tracked point must be within the tracker gimbal limits at all times, and thus will probably be limited to somewhere between 45 and 60, depending on the design of the trackers.

The velocity (V,, V V is the negative of the ground velocity. Thus, a head wind causes an increase in V a down wind increases V and a wind from the left side increases V To get an indication of the magnitude of these components, note that V, is approximately the crosswind V, is approximately a U V, is approximately U where U is the aircraft true airspeed, and a is the aircraft angle of attack.

Thus, by comparing the sections on ballistic equations and aircraft-target velocity (Technically V} V, I

V where v, is the ejection velocity, but for reasonable ejection, the v, can be neglected here; it is included in the effective direction of bomb initial velocity by use of v lv as an angle.)

r ga a Secav (4l) and Consider the definition of (1 a,,, and a For practical purposes these are all the same for a nonrolled aircraft (unless slow airspeed and large, upward wing velocities are present). Thus,

The angle or, is a small angle, particularly when the aircraft is not pulling several 3 acceleration. The subscript is dropped for ease in writing.

The last factor in equation 33 is approximately 1, and thus the equation can be used as k) "(W ow/ a) (44) when used in second order terms of the bombing system equation.

Using the above, for equations 33 and 36 and a relationship of the variables at the release time (A subscript r is used to denote this.) Thus,

sin (B cos (b) ir ir cos p,

V, cos ((1 cos o) (D4) Combining this equation with equations 1 and 3 gives ghqb, cos 0, cos (a cos Q) 7 r T V,:[ oiscgxlcos 10 w" I 2H'Vr cos 6: br (05) (5w where a and e, are small and w, cos ,0 1 1(w;/w sin b sin (0-0: cos .i 1a cos tan 0 M (46) 15 tan (BF-a cos i5) I i 6, cos 1/, r The component of range (r) to tracked point in the :1 tan (0,-a cos 4) (56) e,, e plane is (see FIGS. 4 and 5) r r cos/3 Thus,

( 1-a cos 4: tan 0 1 (o /m tan ipsin (0-0: cos

Using the spherical trigonometric equation sinO sinB cosfl and the fact that a and e, are small and 0 is not too large,

m results (4 results where (1-a cos c tan 0) sec 6,

1 (m /an) sin 0 sin (0 a COS c5) BOMBlNG SYSTEM EQUATIONS ln a bombing attack, note that the proper time to release a bomb is when B (computed) =fi,, (measured) (51) R (computed) Rn.I (measured) (52) cos (a cos d cos a, Q,

cos 0 cos 6, (53) Note that this is the required azimuth lead even if the 5 tracker is not tracking the target.

For the elevation lead angle consider equation 49. Here, if the target was being tracked, the equation gives Compare equation 54 with the actual measured (47) 20 quantities when some point near the target is being tracked.

sin (B a cos 4:) w t- H cos #1 (57) Assume the target and the tracked point are at the same altitude (Assume that these are close together, i.e., one is not dealing with large offset bombing).

0 Then r sin d-B2) Rewriting (The left side of equation 61 can be writfor weapon release 50 ten as 521- B2 B where 1-0; cos tan 6) sec 5, 1 (w,/w,) sin I! sin (0a cos 5) (Equation 50) These equations give the elevation lead angle [3,, since all the other quantities in the equations are measurable.

Rewriting equation 53 for the' azimuth lead angle gives Generally, the lead angles are given in terms of I and 0,. Using the spherical trigonometric relations sin0,-= sinB,,. cos [3,, (63) and tanzl1,= tanfl, secfi (64) tan0,= tanB cos ill, (65) and sin\1:,= sinB sec0,. (66) and in aircraft coordinates the lead angles A, and A, are

sink, +sin cos4 sinili, cos6 sin4 (67) and sink, (-sinO, sin sinip cost) cos) seek, 68 Thus, the computed lead angles for the CIP are obtained from. equations 6l 62, 63, 64, 67, and 68, along with the added relations, equations 2, 3, 4, 5, 7, and 50.

If time of flight is explicitly needed, it is available by combining equations 6, 54, 55, and 56 (or directly from ballistic equations) It can be shown that the angle of fall at impact r, is given by tan 'r itan STICK BOMBING Using HO. 6 where F is the desired first bomb impact, L is the last bomb impact (six bombs in the stick) and represents the target,

s sin a, s sin (a,+e,)

sine,=

and

(N1) s- 2 AX (N1)AX sin (0,41,) "2 R, 71)

where e, is the change in elevation lead angle .1. for the stick bombing case, AX is the bomb spacing, and N is the number of bombs.

Rewriting equation 54 results in R V cos (a cos 45) sin (B -a cos For practi cal purposes the e, in sin (0', 6,) will be neglected. Thus, for elevation lead angle B Ba B2r+ (15) The azimuth lead is the same as for a single release since the center of the stick should be correct in azimuth.

The'above provides the first bomb release condition. Now consider a time-based release of the rest of the stick. The approach taken here is also aimed at being compatible with the automatic release operation. Using equation 54 gives sin (B2t" 00$ 4 'it t where subscript t refers to the target and where some small quantities are neglected. From FIG. 6

combining the last two equations, and remembering that e, is small Sin t+fl2t cos sin 0', sin (B -a cos 5) Combining this equation 74 gives approximately ar 4V, sin (B -wt cos cos 5,

49 (or 54), but neglecting factors near I,

i*( /R) 0) where =B2 =-'n (8n and 17=8 +acos (82) With the assumption that V does not change much in magnitude during the stick release,

tan 5, tan .2

13 where 1' is the flight path angular rate in the vertical plane (e e During the time of a stick release one can assume 1' and g are constant in equation 83. This provides two solutions for w zone for 1' and one for 1794).

"i il M -2),, tan 3 exp (vit/ tan 5) for (8 The first of these can be written as "i u 1/ u) u Using equation 83, the second an equation can be written as Thus, one can use the following equation for either 1' 0 #1 for the time(AT) between the bomb releases of the stick:

(N-1) AT (war- 2 as V This may be used in the form The stick release equations are the normal singlebomb case plus equations 74, 79, and 92.

BOMB RELEASE DELAY AND EJECTION RELEASES The release point must be anticipated by an amount of time, t in order to account for the delay in bomb release. To do this, (The other quantities that are affected by this small delay have a minor effect on the results.) one uses in place of the measured angular rate (0,, the estimated rate in That is, w, is replaced by w =an+dnt (93) in the elevation lead angle equation 61 and where d), is Computed r y??? squats!) t The effect of ejection velocity of the bomb has been included in the elevation computation by 6,. This is the effective change in release angle due to ejectiomlt is a/ 1) b where V, is the ejection velocity.

The azimuth lead should include the azimuth component of this velocity. That is, equation 46 needs the term (This assumes neglecting the difference-in sideways ejection in such bomb racks as the MER/TER. These racks are more useful in stick releases.)

V, sin (96) added to it. Thus, to correct all the azimuth lead equa- I tion the quantity sinili would be replaced by V, cos il/ sin 4 iiiifieifie esw or, for practical purposes replace sinill by siml: V, sin (9a) In actual use the V, sindv term should be used in the azimuth lead equation with a delay-smoothing function operating on the sin factor. This term has a destabilizing or noisy effect on the azimuth signal and thus presents a tracking problem for the pilot.

AUTOMATIC RELEASE (CIP DISPLAY) i id it where an, is given by equation 55.

An alternate method of computing release is used when the measured angle (3,) is the value computed (B,,), or, at release,

I release,

B2 Bu EQUATION SUMMARY The basic equations for a Cl? delivery are equations 2, 50, 56, 61 62, 63, 64,67, 68,74, 75, 79, 92, and 93. w Sm w H cos 1.0 7

cos (01 cos 4:) cos (6.+ 3 ,)4 cos 0 cos (6.+a cos +e,)

sin (fin-a cos sin (ad-B cos (6,+a cos +e,) h sin (B2L! cos Sin t-H 2) cos d-Bar) Y (].-a cos 4 tan 0) set: 13 V 1- (m /m sin I! sin (0a cos 4 (103) sin e,=

id "1+ 1 n (107) vr= W111 nus a mi B") 2 sin), sinB, cosfl cos4 sinfi sind 1 1 1 sink (sinB cosfi sin sinB cosqi) seclt 12 Instead of using the coordinates of the section on aircraft-target velocity, the tracker coordinates shown in FIG. 7 may be used. Here the first rotation is about the I 1nto the alternate trackercoordinates.) For automatic horizontal axis and the second rotation is about the (traclcer) vertical axis. This coordinate system is used in the functional block diagram of theeomputer of H6. 8. Thus the transformation between i, j, k and e e e, is I cos 1 0 sin 1 i e; sin 5 sin n cos 5 --sin t; cos 1 j 0; cos 5 sin 1 sin ti cos {5 cos 17 k Therefore, the velocity the e coordinates are V my cos'r i sim' 120) V,= my sinE sim' w r cosE isinf cosn 121 V =-w,r cosf sim anrsin i' cosfi cosr 122 Combining these as in the section on aircraft-target velocity gives l, V;,[ soc 1 sin (5 I111) +500 1 sin 1; cos -0 o] These relations are the basic equations for an angular rate bombing system.

Using methods set forth previously gives the complete system equations as follows.

sin 1 Hill (E-iwx +8! 11 (SOS (Ed-ar t, cos mcos (Ed-E.) I mm (ros n nos (B, 1512) (hm) m =w +co t [rewritten as 003d =w h, (combine Equations 132 and 136) where H (Equation 137 is the same as equation 83 transformed id il- .s .sv (138) The sight display (ClP mode) uses the angles Q and 35 1 Also CHOSEN RELEASE RANGE (CRR/A) The following paragraphs describe how to include in an angular rate bombing system an operational mode that will arrange for a release at a (pilot) prechosen slant range. Alternatively, in other delivery modes it will indicate what range (or modified to provide altitude) from target the release will occur.

Wen high accuracy in retarded bomb delivery (This delivery will also produce good results using low drag bombs, of course.) is necessary, the ground fire is at an acceptable level to allow the pilot some tracking time. This tracking time need not be long unless the pilot locks on and tracks from a long way out-which is unnecessary.

Assume a straight-line path from shortly after lockon until release. (This to be modified to a possible upward curved course later.) Then siny=(R,./R) sin'y, 140) 5 where the quantities are defined in H6. 10. Using the alternate coordinate system:

" own The elevational lead angle is the value of 5 (or in the main body of the report computed from 'y.

The'azimuth lead angle computation is the same as in all the other modes.

The (CRR/A) mode requires that the target be tracked in elevation and an automatic release is necessary.

if a positive g curved course is desired, the equation is written as 1= t r/ r)" r/ 45) where n 0.5 for a curved course, and usually n l for desirable courses. Y

For a digital computer one could use to obtain a similar result sin v= i (146) where 0.5sn l.

COMPUTED RANGE AT RELEASE in other delivery modes whenever the target is tracked (in elevation) equation 142 above can be used to compute the range at which release will occur if the pilot continueson in the same manner.

r=( v/ WM) 41) FIG. 8 (FIGS. 8A, 8B, 8C and 8D taken together) and FIG. 9 correlate the computational process carried out in the computer with the various inputs thereto. FIG. 8 is a schematic diagram illustrating the intercon-' nection between operational amplifiers and shaping circuits with inputs thereto and resultant outputs therefrom. The symbology used on the input and output lines corresponds to that used in the equations supra. The symbol(s) on the input lines to a particular circuit element represent the signals coupled thereto while the symbol(s) on the output line(s) represent(s) the input signal(s) after being operated on or transformed by the particular circuit element.

H6. 9 is a computational sub-section block diagram derived from FIG. 8 which sets forth wherein the computer various equations are treated.

What is claimed is:

1. ln an angular rate bombing system for use with an aircraft for providing an automatic weapon-release signal without a range to target measurement, inertial velocity-of-aircraft measurement or true-altitude-overtarget measurement whenever the measured (elevation) rate of the line-of-sight to the target equals the computed rate necessary to obtain a hit;

a tracker carried by said aircraft and providing outputs corresponding to angular rates 0),, w, and angles f, 1;;

vertical reference means carried by said aircraft and furnishing outputs corresponding to pitch 8 and roll true airspeed measuring means on said aircraft furnishing an output corresponding to magnitude of velocity (U);

true airspeed measuring means on said aircraft furnishing an output corresponding to magnitude of velocity U)j computer means carried by said aircraft operatively receiving the outputs from the automatic tracker, vertical reference means andtrueairspeed means and for calculating outputs corresponding to the azimuth and elevation lead angles necessary to obtain a hit and to cause automatic weapon release.

2. The system as set forth in claim 1 and further including;

sight unit means carried by said aircraft;

said sight unit operatively receiving the outputs from said computer means corresponding to azimuth and elevation lead angles and displaying them on said sight unit as a computed impact point.

3. The system as set forth in claim 1 further includangle of attack measuring means carried by said aircraft and furnishing an output signal corresponding to aircraft angle of attack a V V a cos d: which signal is also inputted to said computer means and used to compute sin 1 (Dir/(0m), sin 5,,

( Lm hr", wn tllr. 4) and 1- as set forth in equations 126l30, 134, 136, 2. 7' and l42 respectively.

4. The system as set'forth in claim 3 and further including;

pressure altitude measuring means for measuring barometric pressure and outputting a signal corresponding thereto;

said output signal being inputted to said computer means for computing air drag on a released weapon.

5. The'system as set forth in claim 3 and further including;

normal acceleration measuring means for measuring aircraft acceleration and outputting a signal corresponding to k,

said signal being inputted to said computer means and used to compute Q as set forth in equation 137. 

1. In an angular rate bombing system for use with an aircraft for providing an automatic weapon-release signal without a range to target measurement, inertial velocity-of-aircraft measurement or true-altitude-over-target measurement whenever the measured (elevation) rate of the line-of-sight to the target equals the computed rate necessary to obtain a hit; a tracker carried by said aircraft and providing outputs corresponding to angular rates omega i, omega j and angles xi , Eta ; vertical reference means carried by said aircraft and furnishing outputs corresponding to pitch delta and roll phi ; true airspeed measuring means on said aircraft furnishing an output corresponding to magnitude of velocity (U); true airspeed measuring means on said aircraft furnishing an output corresponding to magnitude of velocity (U); computer means carried by said aircraft operatively receiving the outputs from the automatic tracker, vertical reference means and true airspeed means and for calculating outputs corresponding to the azimuth and elevation lead angles necessary to obtain a hit and to cause automatic weapon release.
 2. The system as set forth in claim 1 and further including; sight unit means carried by said aircraft; said sight unit operatively receiving the outputs from said computer means corresponding to azimuth and elevation lead angles and displaying them on said sight unit as a computed impact point.
 3. The system as set forth in claim 1 further including; angle of attack measuring means carried by said aircraft and furnishing an output signal corresponding to aircraft angle of attack Alpha k V2/V3 - Alpha cos phi which signal is also inputted to said computer means and used to compute sin eta r, ( omega ir/ omega id), sin epsilon s, ( omega is/ omega ir), hr 1, omega i, psi r, phi and Tau as set forth in equations 126-130, 134, 136, 2'', 7'' and 142 respectively.
 4. The system as set forth in claim 3 and further including; pressure altitude measuring means for measuring barometric pressure and outputting a signal corresponding thereto; said output signal being inputted to said computer means for computing air drag on a released weapon.
 5. The system as set forth in claim 3 and further including; normal acceleration measuring means for measuring aircraft acceleration and outputting a signal corresponding to kn said signal being inputted to said computer means and used to compute Omega as set forth in equation
 137. 